Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 2, Problem 11RQ
The motor’s transfer function relates armature displacement to armature voltage. How can the transfer function that relates load displacement and armature voltage be determined?
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Please Answer No.1
Consider the translational mechanical network system shown on the figure. A 1-lb force, f(t), si applied at t=0. If fv=1, find K and M such that the response is characterized by a 4-sec settling time and a 1-sec peak time. Also, what is the resulting %OS?
Chapter 2 Solutions
Control Systems Engineering
Ch. 2 - Prob. 1RQCh. 2 - Prob. 2RQCh. 2 - Prob. 3RQCh. 2 - Define the transfer function.Ch. 2 - Prob. 5RQCh. 2 - What do we call the mechanical equations written...Ch. 2 - If we understand the form the mechanical equations...Ch. 2 - Why do transfer functions for mechanical networks...Ch. 2 - What function do gears perform?Ch. 2 - What are the component parts of the mechanical...
Ch. 2 - The motor’s transfer function relates armature...Ch. 2 - Summarize the steps taken to linearize a nonlinear...Ch. 2 - Prob. 1PCh. 2 - Prob. 2PCh. 2 - Prob. 3PCh. 2 - Prob. 4PCh. 2 - Prob. 5PCh. 2 - Prob. 6PCh. 2 - Prob. 7PCh. 2 - A system is described by the following...Ch. 2 - For each of the following transfer functions,...Ch. 2 - Write the differential equation for the system...Ch. 2 - Write the differential equation that is...Ch. 2 - Prob. 12PCh. 2 - Use MATLAB to generate the MATLAB ML transfer...Ch. 2 - Repeat Problem 13 for the MATLAB following...Ch. 2 - Use MATLAB to generate the partial fraction...Ch. 2 - Use MATLAB and the Symbolic Math Symbolic Math...Ch. 2 - Prob. 17PCh. 2 - Prob. 18PCh. 2 - Prob. 19PCh. 2 - Repeat Problem 19 using nodal equations. [Section:...Ch. 2 - Prob. 22PCh. 2 - Prob. 23PCh. 2 - Prob. 24PCh. 2 - Prob. 25PCh. 2 - Prob. 26PCh. 2 - Prob. 27PCh. 2 - Prob. 28PCh. 2 - Prob. 29PCh. 2 - Write, but do not solve, the equations of motion...Ch. 2 - For the unexcited (no external force applied)...Ch. 2 - For each of the rotational mechanical systems...Ch. 2 - For the rotational mechanical system shown in...Ch. 2 - Find the transfer function, 1sTs , for the system...Ch. 2 - For the rotational mechanical system with gears...Ch. 2 - For the rotational system shown in Figure P2.21,...Ch. 2 - Prob. 37PCh. 2 - Find the transfer function, Gs=4s/Ts , for the...Ch. 2 - For the rotational system shown in Figure P2.24,...Ch. 2 - Prob. 40PCh. 2 - Given the rotational system shown in Figure P226,...Ch. 2 - In the system shown in Figure P2.27, the inertia,...Ch. 2 - Prob. 43PCh. 2 - Given the combined translational and rotational...Ch. 2 - Prob. 45PCh. 2 - The motor whose torque-speed characteristics are...Ch. 2 - A dc motor develops 55 N-m of torque at a speed of...Ch. 2 - 48. In this chapter, we derived the transfer...Ch. 2 - Prob. 49PCh. 2 - Find the series and parallel analogs for the...Ch. 2 - Find the series and parallel analogs for the...Ch. 2 - A system’s output, c, is related to the system’s...Ch. 2 - Prob. 53PCh. 2 - Consider the differential equation...Ch. 2 - 55. Many systems are piecewise linear. That is,...Ch. 2 - For the translational mechanical system with a...Ch. 2 - 57. Enzymes are large proteins that biological...Ch. 2 - Prob. 58PCh. 2 - Figure P2.36 shows a crane hoisting a load....Ch. 2 - 60. In 1978, Malthus developed a model for human...Ch. 2 - 61. In order to design an underwater vehicle that...Ch. 2 - 62. The Gompertz growth model is commonly used to...Ch. 2 - A muscle hanging from a beam is shown in Figure...Ch. 2 - A three-phase ac/dc converter supplies dc to a...Ch. 2 - Prob. 65P
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- A dc motor develops 5 N-m of torque at a speed of 75 rad/s when 10 volts are applied. It stalls out at this voltage with 10 N-m of torque. Find the transfer function, G(s) = 02(s)/E.(s). N = 10 ealt) Motor J =1 kg-m2 W= 10 N, = 20 J = 2 kg-m? J, = 2 kg-m- N= 20 Darrow_forwardAssignment 1 A mechanical system with a damper and spring is shown in Figure 1.6. C K Figure 1.6 Damper and spring system a) Obtain the unit step response for the following: 1. damping factor, C = 12 Ns/m and the spring stiffness, K = 36 N/m 2. damping factor, C = 62 Ns/m and the spring stiffness, K = 128.65 N/m 3. damping factor, C = 45 Ns/m and the spring stiffness, K = 425.25 N/m b) Verify in each cases that the calculated time constant (T=C/K) and the one measured from the output step response curve as 63% of the final value are same. c) Obtain the steady state value of the system (t in seconds).arrow_forward2. The equation of motion for a damped multidegree of freedom system is given by Where [m] = [m]{x} + [c]{x} + [k]{x} = {f} [100 = 0 0 0 10 0 10. 1000-4 {f} [c] 8 –4 0 8 – 4 -4 4 0 8 4 = 100 2 0 = Focos(wt) -2 -2 The value of Fo 50N and w 50 rad/sec. Assuming the initial conditions to be zero and using the modal coordinate approach, find out the steady state solution of the system in the modal coordinate for first mode. Plot the steady state solution using the computational tools. 0 −2], [k] = = 2arrow_forward
- What is the damping ratio of the following system transfer function? 27 G (s) = s2+1.8s+9 0.9 0.3 O 0.1arrow_forwardThe transfer function of a dynamical system is written as T(S) = T₁(s)/T₂(s). At 5 rad/s, the gain associated with T₁(S) is 18 dB and the gain associated with T2(S) is 63 dB. Calculate the total gain associated with T(S) at 5 rad/s.arrow_forwardFigure 1 shows an electrical system comprising a series RLC circuit and input voltagesource ein(t).(a) Derive the input-output equation with output y = I and input u = ein(t). (b) Using the derived input-output equation, drive the system transfer function G(s)that relates output to input. Use the following numerical values for the electrical systemparameters: resistance R = 2Ω, inductance L = 0.25H, and capacitance C = 0.4F. (c) Using the derived transfer function, derive the time-domain ordinary differentialequation for the input-output equation of this electrical system. (d) Draw the complete block diagram of this series RLC circuit using the derived transferfunction.arrow_forward
- A spring with a 8-kg mass and a damping constant 2 can be held stretched 0.5 meters beyond its natural length by a force of 1.5 newtons. Suppose the spring is stretched 1 meters beyond its natural length and then released with zero velocity. In the notation of the text, what is the value c2 – 4mk? m'kg/sec? help (numbers) Find the position of the mass, in meters, after t seconds. Your answer should be a function of the variable t with the general form cieat cos(Bt) + cze"s t sin(&t) help (numbers) a = B = * help (numbers) * help (numbers) 8 = * help (numbers) C1 = help (numbers) C2 = 2 help (numbers) kies help us deliver our services. By using our services, you agree to our use of cookies. OK Learn more CONNECT OFF/ON CAPS Charge Po- 14 F4 F5 1- 1+ F6 F7 F8 F9 F10 F11 F12 7 8 R T Y U 5arrow_forwardThe transfer function of the mass-spring-damper system discussed above is determined to be: 100 G(s) = = X(s) F(s) s² + 5s + 100 where x(t) is the displacement of the mass and f(t) is an arbitrary force input. We wish to study how the system responds to changing the frequency of the input, w when the forcing function is a sinusoid f(t) = A sin(wt) with A = 2. As part of your analysis, the following is requested:arrow_forward1. The equations of motion of this system are ÿ + 3y + 4y - 32 - 4Z = 0 Ż +52 +6Z-5ý - 6y = f(t) * = A + Bū y = Cx+Dū Put these equations into state variable form and express the model as a matrix vector equation if output of the system is y. Energy storage element m1 m2 k₁ k₂ State variable *1=ý x₂ = Ż x3 = y x4 =Z k₁ my D k₂ C₂H m₂arrow_forward
- 1. Consider the translational mechanical network system shown on the figure. A 1-lb force, f(t), si applied at t=0. If fv=1, find K and M such that the response is characterized by a 3-sec settling time and a 2-sec peak time. Also, what is the resulting %OS? 2. Given the translational mechanical system shown on the figure, where K=1 and f(t) is a unit step, find the values of M and fv to yield a response with 17% overshoot and a settling time of 5 seconds. f. + M •ƒ(1) oooo K x(1)arrow_forward1.block diagram physical meaning and the time response for different inputsarrow_forwardExample 3: Find the transfer function of the diagram shown below, which contain of a motor coupled to an inertial load through a shaft with a spring constant K. A non-rigid coupling between two mechanical components in a control system often causes torsional resonances that can be transmitted to all parts of the system. MOTOR Jm Bm m K Om K 0₁. LOAD JLarrow_forward
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